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Latin American Symposium on Theoretical Informatics

LATIN 2006: LATIN 2006: Theoretical Informatics pp 781–792Cite as

Exponential Lower Bounds on the Space Complexity of OBDD-Based Graph Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3887))

Abstract

Ordered Binary Decision Diagrams (OBDDs) are a data structure for Boolean functions which is successfully applied in many areas like Integer Programming, Model Checking, and Relational Algebra. Nevertheless, many basic graph problems like Connectivity, Reachability, Single-Source Shortest-Paths, and Flow Maximization are known to be PSPACE-hard if their input graphs are represented by OBDDs. This holds even for input OBDDs of constant width. We extend these results by concrete exponential lower bounds on the space complexity of OBDD-based algorithms for the Reachability Problem, the Single-Source Shortest-Paths Problem, and the Maximum Flow Problem. This involves the first exponential lower bound on the OBDD size for the highest bit of Integer Multiplication w. r. t. the natural interleaved variable order.

An extended version of this paper is available at http://ls2-www.cs.uni-dortmund. de/ sawitzki/.

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Author information

Authors and Affiliations

  1. Computer Science 2, University of Dortmund, D-44221, Dortmund, Germany

    Daniel Sawitzki

Authors
  1. Daniel Sawitzki
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Editor information

Editors and Affiliations

  1. School of Business, Universidad Adolfo Ibáñez, Chile

    José R. Correa

  2. Dept. of Computer Science, University of Chile, Blanco Encalada 2120, 3er piso, Santiago, Chile

    Alejandro Hevia

  3. Dept. Ing. Matemática & Ctr. de Modelamiento Matemático, UMI 2807 U. Chile–CNRS, Chile

    Marcos Kiwi

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Sawitzki, D. (2006). Exponential Lower Bounds on the Space Complexity of OBDD-Based Graph Algorithms. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_71

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  • DOI: https://doi.org/10.1007/11682462_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32755-4

  • Online ISBN: 978-3-540-32756-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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